Problem: Solve for $x$ and $y$ using elimination. ${3x+4y = 50}$ ${-5x-y = -38}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $4$ ${3x+4y = 50}$ $-20x-4y = -152$ Add the top and bottom equations together. $-17x = -102$ $\dfrac{-17x}{{-17}} = \dfrac{-102}{{-17}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {3x+4y = 50}\thinspace$ to find $y$ ${3}{(6)}{ + 4y = 50}$ $18+4y = 50$ $18{-18} + 4y = 50{-18}$ $4y = 32$ $\dfrac{4y}{{4}} = \dfrac{32}{{4}}$ ${y = 8}$ You can also plug ${x = 6}$ into $\thinspace {-5x-y = -38}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ - y = -38}$ ${y = 8}$